Non-Stationary Stochastic Modeling Techniques for Reservoir Description: An Application from the Alaskan North Slope

Abstract

Abstract This paper describes non-stationary (multipopulation) Stochastic Modeling techniques that were developed and used to construct regional average velocity and depth surfaces to the top of a key geological marker overlying several major reservoirs from the Alaskan North Slope. The techniques combine average velocities derived from well data with stacking velocities derived from velocity analyses ("VELANS") of 2D and 3D seismic data. In these techniques, the average velocity field is modeled as a mixture of statistically homogeneous (2nd order stationary) populations that are predominantly consistent with variations in the thickness of a near-surface permafrost layer, and other known geological factors. A multi-population Soft Inversion algorithm is used to infer bounds on average velocities at selected locations (away from existing wells) by statistically calibrating the stacking velocities to the average velocities. Stochastic images of the average velocity field are generated using a new (mixture) Stochastic Imaging algorithm - these images are conditioned to the wells, the Soft Inversion velocity bounds, and to the multi-population spatial correlation model of the data. Finally, seismic travel time measurements are used to convert the average velocity images to depth. The results have been "blind" tested at 30 wells - the results indicate significant improvements in average velocity (and depth) estimation accuracy as compared to conventional interpolation techniques. Introduction Seismic depth conversion may be defined as the process wherein seismic travel time measurements to selected geological horizons are converted (or "migrated") to depth using an inferred spatial velocity field. One class of Stochastic Modeling approaches to seismic depth conversion, typically images depth (measured at the wells) and seismic travel time (measured at and away from the wells) as co-variables, using methods such as external drift and Cokriging/Cosimulation. Such methods typically require significant well control for inference of the underlying spatial auto and cross correlation models for the co-variables; the spatial velocity distribution is modeled only implicitly, and local precision of the estimated depth surfaces relies primarily on the conditioning provided by the well control. In many applications, stacking velocities derived from velocity analyses ("VELANS") of 2D and 3D seismic data are readily available. These stacking velocities often correlate with average velocities, and constitute an important (densely sampled) source of "soft" conditioning information away from the wells, which can augment the available well and seismic travel time information in constructing the desired depth surfaces. This has lead to the development of another class of Stochastic Modeling approaches for seismic depth conversion, wherein the spatial average velocity distribution is explicitly modeled and imaged. P. 67